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Rev Fin 2004; 17:339-378
The Review of Financial Studies Vol. 17, No. 2, pp. 339–378 © 2004 The Society for Financial Studies; all rights reserved.

Conditioning Information and Variance Bounds on Pricing Kernels

Geert Bekaert
Columbia University and NBER

Jun Liu
University of California, Los Angeles

Address correspondence to Geert Bekaert, Columbia Business School, Uris Hall, Room 802, 3022 Broadway, New York, NY 10027, or e-mail: gb241{at}columbia.edu

Gallant, Hansen, and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but suboptimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose an optimally scaled bound that coincides with the GHT bound when the first and second conditional moments are known. When these moments are misspecified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and nonlinear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns.


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 REV FINANC STUDHome page
F. Chabi-Yo
Conditioning Information and Variance Bounds on Pricing Kernels with Higher- Order Moments: Theory and Evidence
Rev. Financ. Stud., January 1, 2008; 21(1): 181 - 231.
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